Main menu

Tags:

ʻOumuamua is the first ever interstellar body that was observed while it passed through our solar system, which makes it a really cool object. Hundreds of thousands of asteroids and comets have been observed, but all of them originated from within our own solar system. It was known that… read more

Tags:

A Hadamard matrix is a matrix with all elements equal to \(+1\) or \(-1\), and for which the rows are mutually orthogonal. If you pick two rows from the matrix and write it as vectors \(\bf x\) and \(\bf y\), then these are orthogonal if… read more

Tags:

What is jerk? Jerk is to acceleration as acceleration is to velocity. And, acceleration is to velocity as velocity is to position. So let’s start there. The instantaneous velocity at which you travel tells you… read more

Tags:

This article shows how to plot the frequency response of the filters that I describe in my articles on filter design. For the specific case of a filter, the frequency response tells you exactly how each frequency is altered. The example code is… read more

Tags:

How many people do you need before the probability that two of them have the same birthday is 50%? The answer to this question is, amazingly, 23. This surprising result is known as the birthday paradox. The word paradox is used here in the sense that… read more

Tags:

In this article, I present the simple idea of exponentiation by squaring. This idea saves computation time in determining the value of large integer powers by “splitting” the exponentiation in a clever way into a series of squaring operations. The technique is based on the fact that… read more

Tags:

Flat tires are random events. However, it seems that the human mind expects random events to be more regular than they actually are. This intuition on randomness might lead to the feeling that your own experience is somehow unexpected or strange, with anecdotes such as “my uncle seems to never have any flats, but my sister had three in the last year alone”. This is related… read more

Tags:

This article explains how to create a windowed-sinc filter with a Kaiser (or Kaiser-Bessel) window. The windowed-sinc filters in previous articles typically had two parameters, the cutoff frequency and the transition bandwidth (or rolloff). With a Kaiser window, there is a third input parameter, the ripple. For the specific case of the Kaiser window, the same… read more